Three of the critical issues in modern cancer research and evolutionary theory include (a) an understanding of the progression of mutations over time, (b) an identification of the cell of origin of these tumors, (c) and the differential response of cancer cell populations to therapy. In this grant proposal, we have created a consortium of investigators that will blend mathematical modeling of the evolutionary dynamics of cancer cells with in vitro and in vivo modeling to validate, and iteratively revise the mathematical frameworks. In the first project we will use evolutionary mathematical modeling to predict the order in which mutations are accumulated during glioma and leukemia development. We will validate our predictions with genetically engineered mouse modeling of these tumors where the temporal order of these mutations is experimentally manipulable. In the second project we will use evolutionary mathematical modeling to predict the most likely cell of origin for gliomas and leukemias. Again, we will use mouse modeling of gliomagenensis and leukemiagenesis that allows us to validate and refine the mathematical models and determine what oncogenes will in fact allow the predicted cells to serve as the origin for these tumors. In the final project, we will use evolutionary theory to describe the differential response to targeted therapy in lung adenocarcinomas and to radiation therapy in medulloblastomas. We will use the mathematical framework to predict the risk of resistance emerging during a particular dosing strategy and determine the optimal approach that will maximally prevent the evolution of resistance. The mathematical framework will again be revised and validated with in vitro and in vivo modeling. These three projects utilize a single cell measurement core facility that allows simultaneous measurements of individual cells for multiple values that impact the mathematical modeling parameters. In the process, we will build a team of interactive investigators that work with other PS-OCs, the NIH, and the outside biologic and mathematical communities. In addition, we have established core education and training curricula to train the next generation of investigators at the interface of these two disciplines.